N-state Potts ices as generalizations of classical and quantum spin ice

TL;DR

This paper introduces N-state Potts ice models as a broad generalization of classical and quantum spin ice, revealing complex gauge fields, excitations, and symmetry effects related to $ ext{su}(N)$ Lie algebras.

Contribution

It provides a unified framework linking N-state Potts ice properties to $ ext{su}(N)$ symmetry and explores quantum generalizations with novel charge interactions.

Findings

Classical N-state Potts ice properties relate to $ ext{su}(N)$ Lie algebras.

Quantum models exhibit charge flavor changing interactions for N>2.

Symmetries cause flux vacuum frustration, affecting excitation dynamics.

Abstract

Classical and quantum spin ice models are amongst the most popular settings for the study of spin liquid physics. $N-$state Potts ice models have been constructed that generalize spin ice, hosting multiple emergent $\text{U}(1)$ gauge fields and excitations charged under non-trivial combinations of these fields. We present a general treatment of classical $N-$state Potts ices relating their properties to the $\mathfrak{su}(N)$ Lie algebras, and demonstrate how the properties of charged excitations in the classical model can be related to this symmetry group. We also introduce quantum generalizations of the Potts Ice models, and demonstrate how charge flavor changing interactions unique to $N>2$ models dominate their low energy physics. We further show how symmetries inherited from the $\mathfrak{su}(N)$ can lead to flux vacuum frustration, greatly modifying the dynamical properties of charged excitations.